10 research outputs found
On the H^1-L^1 boundedness of operators
We prove that if q is in (1,\infty), Y is a Banach space and T is a linear
operator defined on the space of finite linear combinations of (1,q)-atoms in
R^n which is uniformly bounded on (1,q)-atoms, then T admits a unique
continuous extension to a bounded linear operator from H^1(R^n) to Y. We show
that the same is true if we replace (1,q)-atoms with continuous
(1,\infty)-atoms. This is known to be false for (1,\infty)-atoms.Comment: This paper will appear in Proceedings of the American Mathematical
Societ
ON GENERALIZED HYPERINTERPOLATION ON THE SPHERE
Abstract. It is shown that second-order results can be attained by the generalized hyperinterpolation operators on the sphere, which gives an affirmative answer to a question raised by Reimer in Constr. Approx. 18(2002), no. 2, 183–203. 1